{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 生成数据\n",
    "\n",
    "y = Xw+b+c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython import display\n",
    "from mxnet import autograd, nd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_inputs = 2\n",
    "num_examples = 1000\n",
    "true_w = [2, -3.4]\n",
    "true_b = 4.2\n",
    "features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))\n",
    "labels = true_w[0]*features[:, 0] + true_w[1]*features[:, 1] + true_b\n",
    "labels += nd.random.normal(scale=0.01, shape=labels.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(\n",
       " [ 0.5925345 -0.7567092]\n",
       " <NDArray 2 @cpu(0)>, \n",
       " [7.953081]\n",
       " <NDArray 1 @cpu(0)>)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features[1], labels[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "def use_svg_display():\n",
    "    display.set_matplotlib_formats('svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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   ],
   "source": [
    "def set_figsize(figsize=(3.5, 2.5)):\n",
    "    use_svg_display()\n",
    "    plt.rcParams['figure.figsize'] = figsize\n",
    "\n",
    "set_figsize()\n",
    "plt.scatter(features[:, 1].asnumpy(), labels.asnumpy(), 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 读取数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    random.shuffle(indices) # 样本的读取顺序是随机的\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        j = nd.array(indices[i: min(i + batch_size, num_examples)])\n",
    "        yield features.take(j), labels.take(j) #take函数根据索引返回对应元素"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[[-0.4839293   1.3157597 ]\n",
      " [ 1.0956023   0.20017952]\n",
      " [-1.2781463  -0.9593797 ]\n",
      " [ 0.53071696 -0.9929965 ]\n",
      " [-1.0869656   1.7676734 ]\n",
      " [-1.7193607  -0.84718   ]\n",
      " [-1.5240194   1.4221902 ]\n",
      " [ 0.7385103   0.41367826]\n",
      " [-0.29610807 -0.0317046 ]\n",
      " [ 0.20849532 -0.71153325]]\n",
      "<NDArray 10x2 @cpu(0)> \n",
      "[-1.2405584  5.6944942  4.912026   8.659339  -4.0009627  3.6465647\n",
      " -3.682176   4.2803745  3.7175543  7.033284 ]\n",
      "<NDArray 10 @cpu(0)>\n"
     ]
    }
   ],
   "source": [
    "batch_size = 10\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X, y)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "初始化模型参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = nd.random.normal(scale=0.01, shape=(num_inputs, 1))\n",
    "b = nd.zeros(shape=(1,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "w.attach_grad()\n",
    "b.attach_grad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义神经网络模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(X, w, b):\n",
    "    return nd.dot(X, w) + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def squared_loss(y_hat, y):\n",
    "    return(y_hat - y.reshape(y_hat.shape)) ** 2/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义优化算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):\n",
    "    for param in params:\n",
    "        param[:] = param - lr *param.grad/batch_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss0.041051\n",
      "epoch 2, loss0.000160\n",
      "epoch 3, loss0.000050\n",
      "epoch 4, loss0.000050\n",
      "epoch 5, loss0.000050\n"
     ]
    }
   ],
   "source": [
    "lr = 0.03\n",
    "num_epochs = 5\n",
    "net = linreg\n",
    "loss = squared_loss\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        with autograd.record():\n",
    "            l = loss(net(X, w, b), y)\n",
    "        l.backward()\n",
    "        sgd([w, b], lr, batch_size)\n",
    "    train_l = loss(net(features, w, b), labels)\n",
    "    print('epoch %d, loss%f' % (epoch + 1, train_l.mean().asnumpy()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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